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    Optimal control of maize foliar diseases using the plants population dynamics
    (Taylor and Fancis, 2015-09-28) Collins, Obiora Cornelius; Duffy, Kevin Jan
    Pathogens and insects can have important negative effects on yields of crops cultivated by humans. These effects can be important for the food security or financial well-being of individuals. In particular, maize is a very important staple crop worldwide and is vulnerable to diseases. We formulate here a mathematical model to evaluate the impacts of foliar diseases on the population dynamics of maize plants. Qualitative analyses of the important mathematical features of the model are carried out. We show how this methodology can be extended to reducing the spread of foliar diseases through effective control measures with minimum costs.
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    Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold
    (Elsevier, 2016) Duffy, Kevin Jan; Collins, Obiora Cornelius
    The existence, or not, of cyclic dynamics is one of the pivotal aspects of ecological populations. This work considers a consumer resource model found in ecology that can describe both cyclic and non-cyclic dynamics depending on parameter conditions. A threshold consumption number C0 is introduced, similar to the basic reproduction in epidemiological models. It is shown that consumer survival requires C0 > 1 and that a Hopf bifurcation occurs at , where is defined here and is greater than 1. This result is discussed with an example and extensions to other more complicated models.